Data normalization

Initialization

We start the analysis by initializing the packages required for all the analysis performed in this section. We also define the root directory, within which all the input/output operations for this project will be performed. At the end of this document, a detailed software version information is provided for easier reproducibility of the analysis.

Normalization methodology

We use two different normalization strategy to answer specific questions -

  • For a given plate \(i\), the Cytoplasmic and Mitochondrial roGFP2 ratios are normalized by the median of all controls in the same plate i.e for cytoplasm - \[NormCyto(i) = \frac{Cyto_i} {median(Ctrl_i)}\] and for mitochondria, \[NormMito(i) = \frac{Mito_i} {median(Ctrl_i)}\]

This type of control based plate normalization will be suitable in comparing the redox levels in across organells and nutrients since the roGFP2 ratios has been commonly normalized to the plate control.

  • For a given plate \(i\) with the Cytoplasmic and Mitochondrial roGFP2 ratios \(j\) are normalized by their respective plate specific median roGFP2 ratios i.e for cytoplasm - \[NormCyto_{i} = \frac{Cyto_{ij} - median(Cyto_{i})} {mad(Cyto_{i})}\] and for mitochondria, \[NormMito_{i} = \frac{Mito_{ij} - median(Mito_{i})} {mad(Mito_{i})}\]

This type of organelle specific normalization will be suitable in comparing the redox levels in each organelle across all plates. Since this type of normalization tells us how far are the values from the plate median.

Furthermore, for each normalization strategy, we also summarized the quadruplicated values per gene by taking the median of the scaled values. Due to our outlier removal strategy in the previous section, many NA values were introduced. Each mutant has 4 values, we removed mutants with 2 or more NA values and those with only one NA value was substituted with the median of the other 3 observed values. Next, there were also multiple copies of the same mutants (genes) in either the same plate or different plates. We summarized them by taking the set of quadruplicated or median summarized values which have the maximum absolute median value.

Eventually, we generate the following -

  • A table with all the replicate values per organelle and nutrient conditions and the the median summarized value from all plates
  • A matrix with gene/mutants in rows and all combinations of organelle, nutrient and replicates (and median summarized value) in the column

Below is the table of cleaned raw data that we will use in our analysis.

rawDatCleaned = readRDS(paste0(path, "data/workspaces/YeastMutantRedox_RawDataCleaned.RDS"))
rawDatCleaned_ctrlfilt = readRDS(paste0(path, "data/workspaces/YeastMutantRedox_RawData_Outliers_and_PoorControlFiltered.RDS"))

normalizeScreenData = function(normMethod)
{
  
  if(normMethod == "fracControl"){
    normDat = split(rawDatCleaned_ctrlfilt, as.character(rawDatCleaned_ctrlfilt$Type))
    normDat = lapply(normDat, function(x) {
    split(x, x$Plate)})
  }
  
  if(normMethod == "robustZ"){
    normDat = split(rawDatCleaned, rawDatCleaned$Type)
    normDat = lapply(normDat, function(x) {
    split(x, x$Plate)})
  }
  
  normDatReps = normDat
  
  for (i in 1:length(normDat))
  {
    for (j in 1:length(normDat[[i]]))
    {
      tmp = droplevels(normDat[[i]][[j]])
      
      if(nrow(tmp) > 0) #since there are no entries from plate 150, was filtered in previous step
      {
        
      #---------------------------------------------------------------------------------------------
      # Separate Controls, Cytoplasam and Mitochondrial roGFP2 ratios per plate
      #---------------------------------------------------------------------------------------------
      
      # Control
      tmp.ctrl = droplevels(tmp[tmp$Content == "Control",])
      
      # Cytoplasm
      tmp.cyto = droplevels(tmp[tmp$Content == "Cytoplasm",])
      
      # Mitochondria
      tmp.mito = droplevels(tmp[tmp$Content == "Mitochondria",])
      
      rm(tmp)
      
      #---------------------------------------------------------------------------------------------
      # Compute the corresponding normalization factors (median & median absolute deviation)
      #---------------------------------------------------------------------------------------------
      
      # Normalizing factor - Control
      nf.ctrl.med = median(tmp.ctrl$roGFP2.ratio, na.rm = T)
      
      # Normalizing factor - Cytoplasm
      nf.cyto.med = median(tmp.cyto$roGFP2.ratio, na.rm = T)
      nf.cyto.mad = mad(tmp.cyto$roGFP2.ratio, na.rm = T)
      
      # Normalizing factor - Mitochondria
      nf.mito.med = median(tmp.mito$roGFP2.ratio, na.rm = T)
      nf.mito.mad = mad(tmp.mito$roGFP2.ratio, na.rm = T)
      
      #---------------------------------------------------------------------------------------------
      # The two normalization strategies (plate control and median based)
      #---------------------------------------------------------------------------------------------
      
      # Normalization 1 - Plate control based
      if (normMethod == "fracControl")
      {
        tmp.cyto$roGFP2.ratio = tmp.cyto$roGFP2.ratio / nf.ctrl.med
        tmp.mito$roGFP2.ratio = tmp.mito$roGFP2.ratio / nf.ctrl.med
      }
      
      # Normalization 2 - Plate median based
      if (normMethod == "robustZ")
      {
        tmp.cyto$roGFP2.ratio = (tmp.cyto$roGFP2.ratio - nf.cyto.med) / nf.cyto.mad
        tmp.mito$roGFP2.ratio = (tmp.mito$roGFP2.ratio - nf.mito.med) / nf.mito.mad
      }
      
      rm(nf.ctrl.med,
         nf.cyto.med,
         nf.cyto.mad,
         nf.mito.med,
         nf.mito.mad)
      
      #---------------------------------------------------------------------------------------------
      # Normalized data with replicates - coverting from long to wide table format
      #---------------------------------------------------------------------------------------------
      
      #---Cytoplasm---#
      
      tmp.cyto.repl = tmp.cyto %>%
        select(Gene.Symbol, Plate, Group, roGFP2.ratio, Type, Content) %>%
        group_by(Gene.Symbol, Group) %>%
        mutate(pseurep = paste0("roGFP2_ratio_", 1:n())) %>%
        spread(key = pseurep, value = roGFP2.ratio) %>%
        ungroup() %>%
        select(-Group) %>%
        rename(Genes = Gene.Symbol,
               Nutrient = Type,
               Organelle = Content)
      
      #---Mitochondria---#
      
      tmp.mito.repl = tmp.mito %>%
        select(Gene.Symbol, Plate, Group, roGFP2.ratio, Type, Content) %>%
        group_by(Gene.Symbol, Group) %>%
        mutate(pseurep = paste0("roGFP2_ratio_", 1:n())) %>%
        spread(key = pseurep, value = roGFP2.ratio) %>%
        ungroup() %>%
        select(-Group) %>%
        rename(Genes = Gene.Symbol,
               Nutrient = Type,
               Organelle = Content)
      
      #--Compilation---#
      
      normDatReps[[i]][[j]] = rbind(tmp.cyto.repl, tmp.mito.repl)
      
      #Deleting
      rm(tmp.ctrl,
         tmp.cyto,
         tmp.mito,
         tmp.cyto.repl,
         tmp.mito.repl)
      }
    }
   rm(j) 
  }
  rm(i)
 
  res = lapply(normDatReps, function(x) {
    x = do.call("rbind", x)
    x = as.data.frame(x)
    x$Plate     = factor(x$Plate)
    x$Organelle = factor(x$Organelle, levels = c("Mitochondria", "Cytoplasm"))
    x$Nutrient  = factor(x$Nutrient, levels = c("Glucose", "Galactose", "Glycerol"))
    rownames(x) = 1:nrow(x)
    return(x)
  })
  
  res = do.call("rbind", res)
  
  #-------------------------------------------------------------------------------------------------
  # Summarizing mutiple mutants (i.e same gene) from the same or different plates
  # Also dropping genes with 2 or more NA values
  # For genes with just 1 NA value, replacing it with the median of the remaining 3 observed values
  #-------------------------------------------------------------------------------------------------
  
  res = res %>%
    rowwise() %>%
    mutate(Median_roGFP2_ratio = median(c(roGFP2_ratio_1, roGFP2_ratio_2, roGFP2_ratio_3, roGFP2_ratio_4), na.rm=T),
           NA_per_row = sum(is.na(c(roGFP2_ratio_1, roGFP2_ratio_2, roGFP2_ratio_3, roGFP2_ratio_4)))) %>%
    filter(NA_per_row < 2) %>%
    ungroup() %>%
    mutate_at(vars(starts_with("roGFO2_ratio_")),
     function(x) ifelse(is.na(x), .$Median_roGFP2_ratio, x)) %>% 
    select(-NA_per_row) %>% 
    group_by(Organelle, Nutrient, Genes) %>% 
    top_n(n=1, abs(Median_roGFP2_ratio)) %>%
    ungroup()
  
  #-------------------------------------------------------------------------------------------------
  # Compiling all replicates across organelles and nutrient conditions into a single matrix
  #-------------------------------------------------------------------------------------------------
  
  redoxMat = data.table(res[,c("Genes", "Nutrient", "Organelle", "roGFP2_ratio_1", "roGFP2_ratio_2", "roGFP2_ratio_3", "roGFP2_ratio_4")])
  redoxMat = dcast(redoxMat, Genes ~ Organelle + Nutrient, fun.aggregate = function(x){x}, fill=NA,
              value.var = c("roGFP2_ratio_1", "roGFP2_ratio_2", "roGFP2_ratio_3", "roGFP2_ratio_4"))
  redoxMat = redoxMat[,c(1,
               2,8,14,20,
               3,9,15,21,
               4,10,16,22,
               5,11,17,23,
               6,12,18,24,
               7,13,19,25
               )]
  redoxMat = data.frame(redoxMat, stringsAsFactors = F )
  rownames(redoxMat) = redoxMat$Genes
  redoxMat = redoxMat[,-1]
  
  #-------------------------------------------------------------------------------------------------
  # Compiling the median values across organelles and nutrient conditions into a single matrix
  #-------------------------------------------------------------------------------------------------
  
  redoxMat_median = data.table(res[,c("Genes", "Nutrient", "Organelle", "Median_roGFP2_ratio")])
  redoxMat_median = dcast(redoxMat_median, Genes ~ Organelle + Nutrient, fun.aggregate = function(x){x}, fill=NA,
                    value.var = "Median_roGFP2_ratio")
  
  redoxMat_median = data.frame(redoxMat_median, stringsAsFactors = F )
  rownames(redoxMat_median) = redoxMat_median$Genes
  redoxMat_median = redoxMat_median[,-1]
  
  #-------------------------------------------------------------------------------------------------
  # Putting all the results into one
  #-------------------------------------------------------------------------------------------------
  
  res = list(redox_table = res, redox_replicates = redoxMat, redox_median = redoxMat_median)
  rm(normDat, normDatReps, redoxMat, redoxMat_median)
  return(res)
}

normDat.ctrNorm = normalizeScreenData(normMethod = "fracControl")
normDat.Znorm   = normalizeScreenData(normMethod = "robustZ")

Normalized data overview

We normalize the data as described above, below is the summary and the distribution of the normalized data -

  • For per plate normalization based on plate specific control
    Genes               Plate            Nutrient           Organelle    
 Length:26376       102    :  564   Glucose  :8798   Mitochondria:13159  
 Class :character   105    :  562   Galactose:9014   Cytoplasm   :13217  
 Mode  :character   107    :  555   Glycerol :8564                       
                    116    :  554                                        
                    118    :  553                                        
                    142    :  545                                        
                    (Other):23043                                        
 roGFP2_ratio_1     roGFP2_ratio_2     roGFP2_ratio_3     roGFP2_ratio_4   
 Min.   :0.000219   Min.   :0.000227   Min.   :0.000225   Min.   :0.00022  
 1st Qu.:1.257943   1st Qu.:1.252091   1st Qu.:1.243790   1st Qu.:1.24571  
 Median :1.574910   Median :1.569008   Median :1.561554   Median :1.56213  
 Mean   :1.630336   Mean   :1.626620   Mean   :1.623120   Mean   :1.62213  
 3rd Qu.:1.939161   3rd Qu.:1.939125   3rd Qu.:1.935817   3rd Qu.:1.92914  
 Max.   :6.984722   Max.   :7.126663   Max.   :7.204534   Max.   :7.25000  
                                                          NA's   :177      
 Median_roGFP2_ratio
 Min.   :0.000227   
 1st Qu.:1.259919   
 Median :1.563700   
 Mean   :1.625279   
 3rd Qu.:1.930953   
 Max.   :6.225727
  • For per plate normalization based on median organelle specific values
    Genes               Plate            Nutrient           Organelle    
 Length:27695       102    :  564   Glucose  :9192   Mitochondria:13807  
 Class :character   105    :  564   Galactose:9246   Cytoplasm   :13888  
 Mode  :character   110    :  563   Glycerol :9257                       
                    116    :  561                                        
                    113    :  559                                        
                    114    :  559                                        
                    (Other):24325                                        
 roGFP2_ratio_1      roGFP2_ratio_2       roGFP2_ratio_3     
 Min.   :-14.18291   Min.   :-14.180302   Min.   :-17.29949  
 1st Qu.: -0.64326   1st Qu.: -0.674491   1st Qu.: -0.69362  
 Median :  0.03188   Median :  0.002007   Median : -0.02326  
 Mean   :  0.05993   Mean   :  0.035221   Mean   :  0.01129  
 3rd Qu.:  0.69614   3rd Qu.:  0.681601   3rd Qu.:  0.66520  
 Max.   : 27.78831   Max.   : 27.774188   Max.   : 28.68528  
                                                             
 roGFP2_ratio_4     Median_roGFP2_ratio
 Min.   :-9.92714   Min.   :-9.61836   
 1st Qu.:-0.67574   1st Qu.:-0.54478   
 Median :-0.01056   Median :-0.01878   
 Mean   : 0.01211   Mean   : 0.03033   
 3rd Qu.: 0.65572   3rd Qu.: 0.55489   
 Max.   :27.81965   Max.   :27.78125   
 NA's   :255
  • Number of mutants per condition
   GalactoseCytoplasm GalactoseMitochondria      GlucoseCytoplasm 
                 4519                  4495                  4416 
  GlucoseMitochondria     GlycerolCytoplasm  GlycerolMitochondria 
                 4382                  4282                  4282
  • Similarity between the normalization strategies
plotList = vector("list", 6)
names(plotList) = c("Glucose-Cytoplasm",   "Glucose-Mitochondria",
                    "Galactose-Cytoplasm", "Galactose-Mitochondria",
                    "Glycerol-Cytoplasm",  "Glycerol-Mitochondria")

plotListTop = plotList

for(i in c("Glucose", "Galactose", "Glycerol"))
{
  for(j in c("Cytoplasm", "Mitochondria"))
  {
    a = normDat.Znorm$redox_table[which(normDat.Znorm$redox_table$Nutrient == i & normDat.Znorm$redox_table$Organelle == j),]
    a = a[, c("Genes", "Median_roGFP2_ratio")]
    colnames(a) = c("Genes", "Znorm")
    
    b = normDat.ctrNorm$redox_table[which(normDat.ctrNorm$redox_table$Nutrient == i & normDat.ctrNorm$redox_table$Organelle == j),]
    b = b[, c("Genes", "Median_roGFP2_ratio")]
    colnames(b) = c("Genes", "Ctrlnorm")
    
    df = merge(a,b)
    
    topZ = quantile(df$Znorm, probs = c(0.05, 0.95))
    topC = quantile(df$Ctrlnorm, probs = c(0.05, 0.95))
    
    df_top = df[which(df$Znorm < topZ[1] | df$Znorm > topZ[2] | df$Ctrlnorm < topC[1] | df$Ctrlnorm > topC[2]),]
    
    id = paste(i,j,sep="-")
    
    plotList[[id]] = ggscatter(df, x = "Znorm", y = "Ctrlnorm",
                               color = "black", shape = 20, size = 0.5, # Points color, shape and size
                               add = "reg.line",  # Add regressin line
                               add.params = list(color = "blue", fill = "lightgray"), # Customize reg. line
                               conf.int = TRUE, # Add confidence interval
                               cor.coef = TRUE, # Add correlation coefficient. see ?stat_cor
                               cor.coeff.args = list(method = "spearman", label.x = -10, label.y = 3.5, label.sep = "\n"),
                               ggtheme = theme_classic(base_size = 8)) + labs(subtitle = id)
    
     plotListTop[[id]] = ggscatter(df_top, x = "Znorm", y = "Ctrlnorm",
                               color = "black", shape = 20, size = 0.5, # Points color, shape and size
                               add = "reg.line",  # Add regressin line
                               add.params = list(color = "blue", fill = "lightgray"), # Customize reg. line
                               conf.int = TRUE, # Add confidence interval
                               cor.coef = TRUE, # Add correlation coefficient. see ?stat_cor
                               cor.coeff.args = list(method = "spearman",  label.x = -10, label.y = 3.5, label.sep = "\n"),
                               ggtheme = theme_classic(base_size = 8)) + labs(subtitle = id)
    
    
    rm(a, b, df,df_top, topZ, topC, id)
  }
  rm(j)
}
rm(i)

Plotting the correlation between the two normalization techniques for all matching mutants

Plotting the correlation between the two normalization techniques using ONLY the top hits 5% (high/low) roGFP2 ratios from either normalization method

Sample similarity - Dimensionality reduction

Next, we apply the dimensionality reduction method Multidimesional scaling (MDS) on the roGFP2 ratio values normalized by the plate control and Robust Z normalized to identify the major grouping of the yeast mutants based on their redox status across organelle and nutrient conditions. We distinctly see that the redox status is different between the organelles (also seen by density plots, higher in mitochondria compared to cytoplasm) and within the organelles the mutants group by the nutrient conditions.

getMDSdata = function(dat) {
    mds = cmdscale(dist(t(dat)), eig = TRUE, k = 2)$points
    colnames(mds) = c("MDS1", "MDS2")
    
    col_anno = do.call("rbind", strsplit(rownames(mds), "_"))
    col_anno = col_anno[, -c(1:3)]
    colnames(col_anno) = c("Compartment", "Nutrient")
    mds = data.frame(mds, col_anno)
}

mdsZ = getMDSdata(dat = normDat.Znorm$redox_replicates)
mdsC = getMDSdata(dat = normDat.ctrNorm$redox_replicates)

p1 = ggplot(mdsZ, aes(x = MDS1, y = MDS2)) + theme_classic(base_size = 8) + labs(subtitle = "Robust Z normalized") + 
    geom_point(aes(color = Nutrient, shape = Compartment), size = 2) + scale_color_manual(values = c("#fc8d62", 
    "#66c2a5", "#8da0cb"))

p2 = ggplot(mdsC, aes(x = MDS1, y = MDS2)) + theme_classic(base_size = 8) + labs(subtitle = "Plate control normalized") + 
    geom_point(aes(color = Nutrient, shape = Compartment), size = 2) + scale_color_manual(values = c("#fc8d62", 
    "#66c2a5", "#8da0cb"))

pA = p1 + p2 + plot_layout(guides = "collect")

p3 <- ggviolin(normDat.Znorm$redox_table, x = "Organelle", y = "Median_roGFP2_ratio", 
    xlab = "", ylab = "Median roGFP2 ratio", draw_quantiles = 0.5, fill = "Organelle", 
    facet.by = "Nutrient", color = "grey90") + stat_compare_means(label = "p.format", 
    method = "wilcox", cex = 2) + labs(subtitle = "Robust Z normalized") + theme_classic(base_size = 8) + 
    theme(legend.position = "right", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + 
    scale_fill_manual(values = c("#b2df8a", "#7570b3"))


p4 <- ggviolin(normDat.ctrNorm$redox_table, x = "Organelle", y = "Median_roGFP2_ratio", 
    xlab = "", ylab = "Median roGFP2 ratio", draw_quantiles = 0.5, fill = "Organelle", 
    facet.by = "Nutrient", color = "grey90") + stat_compare_means(label = "p.format", 
    method = "wilcox", cex = 2) + labs(subtitle = "Plate control normalized") + theme_classic(base_size = 8) + 
    theme(legend.position = "right", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + 
    scale_fill_manual(values = c("#b2df8a", "#7570b3"))

pB = p3 + p4 + plot_layout(guides = "collect")

p5 = ggviolin(normDat.Znorm$redox_table, x = "Nutrient", y = "Median_roGFP2_ratio", 
    xlab = "", ylab = "Median roGFP2 ratio", draw_quantiles = 0.5, fill = "Nutrient", 
    facet.by = "Organelle", color = "grey90") + stat_compare_means(method = "anova", 
    label.y = 22, label.x = 1.5, cex = 2) + stat_compare_means(label = "p.signif", 
    method = "wilcox", ref.group = ".all.", hide.ns = TRUE) + scale_fill_manual(values = c("#66c2a5", 
    "#fc8d62", "#8da0cb")) + labs(subtitle = "Robust Z normalized") + theme_classic(base_size = 8) + 
    theme(legend.position = "right", axis.text.x = element_blank(), axis.ticks.x = element_blank())

p6 = ggviolin(normDat.ctrNorm$redox_table, x = "Nutrient", y = "Median_roGFP2_ratio", 
    xlab = "", ylab = "Median roGFP2 ratio", draw_quantiles = 0.5, fill = "Nutrient", 
    facet.by = "Organelle", color = "grey90") + stat_compare_means(method = "anova", 
    label.y = 5, label.x = 1.5, cex = 2) + stat_compare_means(label = "p.signif", 
    method = "wilcox", ref.group = ".all.", hide.ns = TRUE) + scale_fill_manual(values = c("#66c2a5", 
    "#fc8d62", "#8da0cb")) + labs(subtitle = "Plate control normalized") + theme_classic(base_size = 8) + 
    theme(legend.position = "right", axis.text.x = element_blank(), axis.ticks.x = element_blank())

pC = p5 + p6 + plot_layout(guides = "collect")

p = pA/pB/pC

ggsave(filename = paste0(path, "analysis/normalization/roGFP2_ratio_comparison_nutrient_compartments.pdf"), 
    plot = p, width = 7, height = 7)

p

Replicate similarity - Correlation

Below we show the correlation among replicates.

  • first with plate median (nutrient specific) based Robust Z normalization

  • second with control based normalization

Distribution of normalized data

  • For per plate normalization based on plate specific control and an interactive data table to access the data

  • For per plate normalization based on median organelle specific values and an interactive data table to access the data

Session information

R version 3.6.2 (2019-12-12)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.16

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] RColorBrewer_1.1-2 pheatmap_1.0.12    patchwork_1.0.0    ggpubr_0.2.4      
 [5] magrittr_1.5       ggrepel_0.8.1      WriteXLS_5.0.0     data.table_1.12.8 
 [9] forcats_0.4.0      stringr_1.4.0      dplyr_0.8.4        purrr_0.3.3       
[13] readr_1.3.1        tidyr_1.0.2        tibble_2.1.3       ggplot2_3.2.1     
[17] tidyverse_1.3.0    DT_0.12            rmdformats_0.3.6   knitr_1.28        

loaded via a namespace (and not attached):
 [1] httr_1.4.1        jsonlite_1.6.1    modelr_0.1.5      shiny_1.4.0      
 [5] assertthat_0.2.1  cellranger_1.1.0  yaml_2.2.1        pillar_1.4.3     
 [9] backports_1.1.5   lattice_0.20-38   glue_1.3.1        digest_0.6.23    
[13] promises_1.1.0    ggsignif_0.6.0    rvest_0.3.5       colorspace_1.4-1 
[17] htmltools_0.4.0   httpuv_1.5.5      plyr_1.8.5        pkgconfig_2.0.3  
[21] broom_0.5.4       haven_2.2.0       bookdown_0.17     xtable_1.8-4     
[25] scales_1.1.0      later_1.0.0       generics_0.0.2    farver_2.0.3     
[29] ellipsis_0.3.0    withr_2.1.2       lazyeval_0.2.2    cli_2.0.1        
[33] mime_0.9          crayon_1.3.4      readxl_1.3.1      evaluate_0.14    
[37] fs_1.3.1          fansi_0.4.1       nlme_3.1-144      xml2_1.2.2       
[41] tools_3.6.2       hms_0.5.3         formatR_1.7       lifecycle_0.1.0  
[45] munsell_0.5.0     reprex_0.3.0      compiler_3.6.2    rlang_0.4.4      
[49] grid_3.6.2        rstudioapi_0.11   htmlwidgets_1.5.1 crosstalk_1.0.0  
[53] labeling_0.3      rmarkdown_2.1     gtable_0.3.0      DBI_1.1.0        
[57] reshape2_1.4.3    R6_2.4.1          lubridate_1.7.4   fastmap_1.0.1    
[61] stringi_1.4.5     Rcpp_1.0.3        vctrs_0.2.2       dbplyr_1.4.2     
[65] tidyselect_1.0.0  xfun_0.12

Ashwini Kumar Sharma, PhD

2021-06-11